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Journal of Dynamical and Control Systems

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14.04.2016

On Sub-Riemannian and Riemannian Structures on the Heisenberg Groups

verfasst von: Rory Biggs, Péter T. Nagy

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 3/2016

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Abstract

We consider the left-invariant sub-Riemannian and Riemannian structures on the Heisenberg groups. A classification of these structures was found previously. In the present paper, we find (for each normalized structure) the isometry group, the exponential map, the totally geodesic subgroups, and the conjugate locus. Finally, we determine the minimizing geodesics from identity to any given endpoint. (Several of these points have been covered, to varying degrees, by other authors.)

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Titel: On Sub-Riemannian and Riemannian Structures on the Heisenberg Groups
verfasst von: Rory Biggs
Péter T. Nagy
Publikationsdatum: 14.04.2016
Verlag: Springer US
Erschienen in: Journal of Dynamical and Control Systems / Ausgabe 3/2016
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-016-9316-9

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